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Chemistry Question on Chemical Kinetics

For the following homogeneous reaction, the unit of rate constant is: A+B−>[k]CA+B {->[k]}C

A

mol−1L s−1 mol^{-1}L\,s^{-1}

B

s−1s^{-1}

C

ss

D

s−1mol L−1s^{-1}mol\,L^{-1}

Answer

mol−1L s−1 mol^{-1}L\,s^{-1}

Explanation

Solution

For the homogenous gaseous reaction, A+B−>[k]CA+B {->[k]}C, the rate law is dxdt=k[A][B]\frac{d x}{d t} =k[A][B] or k=dxdt×[A][B]k =\frac{d x}{d t \times[A][B]} =mol L−1 time ×mol L−1×mol L−1=\frac{mol\, L^{-1}}{\text { time } \times mol\, L^{-1} \times mol\, L^{-1}} or unit of rate constant k is mol−1 L time−1mol ^{-1}\, L\, time^{-1} or mol−1 L s−1mol^{-1}\,L\,s^{-1}